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Anestetic [448]
3 years ago
5

5 boys and 6 girls attend a birthday party and play pin the tail on the donkey. If a girl wins first and second place and a boy

wins third place, How many different arrangements of first, second, and third are there? =
Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
5 0

Answer:

75 Arrangements

Step-by-step explanation:

Girl can secure 1st & 3rd, boy can secure 2nd position in : 6 x 5 x 5 = 150 ways ; As :

  • 1st position holder can be chosen in 6 ways (among 6 girls)
  • 2nd position holder can be chosen in 5 ways (among 5 boys)
  • 3rd position holder can be chosen in ( among 5 remaining girls)

The arrangement of first, second & third  :

It is same : If Girl G1 gets first rank & Girl G2 gets third rank, is same as ; Girl G1 gets third rank & Girl G2 gets first rank. So, two are considered the same group. Hence, number of arrangements are 150 / 2 = 75  arrangements.

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Triangular numbers can be represented with equilateral triangles formed by dots. The first five triangular numbers are 1, 3, 6,
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Position in the sequence    triangular number    relation

1                                          1                              1 = 1*(1+1)/2

2                                          3                              3 = 2(2+1)/2

3                                          6                              6 = 3(3+1)/2

4                                         10                            10 = 4(4+1)/2

5                                         15                              15= 5(5+1)/2

Call n the position in the sequence, then the triangular number is: n(n+1)/2
 



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3 years ago
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